Majoro came on to score the second goal of the Group A win over Angola in Durban but was carried off on a stretcher late in the game after a collision with opposing goalkeeper Lama.
"I'm going to miss maybe a couple of games. I have seven or so stitches in my leg. The medical team said I may miss the next game or two," he told reporters.
Majoro's absence adds to the injury list for South Africa who were unable to field midfielders Kagisho Dikgacoi and Lerato Chabangu in the 2-0 win.
The hosts next face Morocco in Durban on Sunday in a decisive tie for both countries.